jmc

Question

Twenty-seven solid gold spherical beads each of radius 3 are melted down and recast into a larger, solid gold sphere. How many units are in the radius of this larger gold sphere?

Accepted Answer

Each spherical bead has volume 43(3^3)=4 3^2, so the twenty-seven beads have total volume 4 3^2 27 = 4 3^5 . Let the larger sphere have radius r units, so we have 43 r^3 = 4 3^5. Simplifying gives r^3 = 3^6 or r=3^2=9.